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  <div class="section" id="numpy-linalg-cond">
<h1>numpy.linalg.cond<a class="headerlink" href="#numpy-linalg-cond" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.linalg.cond">
<code class="sig-prename descclassname">numpy.linalg.</code><code class="sig-name descname">cond</code><span class="sig-paren">(</span><em class="sig-param">x</em>, <em class="sig-param">p=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/linalg/linalg.py#L1647-L1763"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.linalg.cond" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the condition number of a matrix.</p>
<p>This function is capable of returning the condition number using
one of seven different norms, depending on the value of <em class="xref py py-obj">p</em> (see
Parameters below).</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>x</strong><span class="classifier">(…, M, N) array_like</span></dt><dd><p>The matrix whose condition number is sought.</p>
</dd>
<dt><strong>p</strong><span class="classifier">{None, 1, -1, 2, -2, inf, -inf, ‘fro’}, optional</span></dt><dd><p>Order of the norm:</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>p</p></th>
<th class="head"><p>norm for matrices</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>None</p></td>
<td><p>2-norm, computed directly using the <code class="docutils literal notranslate"><span class="pre">SVD</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>‘fro’</p></td>
<td><p>Frobenius norm</p></td>
</tr>
<tr class="row-even"><td><p>inf</p></td>
<td><p>max(sum(abs(x), axis=1))</p></td>
</tr>
<tr class="row-odd"><td><p>-inf</p></td>
<td><p>min(sum(abs(x), axis=1))</p></td>
</tr>
<tr class="row-even"><td><p>1</p></td>
<td><p>max(sum(abs(x), axis=0))</p></td>
</tr>
<tr class="row-odd"><td><p>-1</p></td>
<td><p>min(sum(abs(x), axis=0))</p></td>
</tr>
<tr class="row-even"><td><p>2</p></td>
<td><p>2-norm (largest sing. value)</p></td>
</tr>
<tr class="row-odd"><td><p>-2</p></td>
<td><p>smallest singular value</p></td>
</tr>
</tbody>
</table>
<p>inf means the numpy.inf object, and the Frobenius norm is
the root-of-sum-of-squares norm.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>c</strong><span class="classifier">{float, inf}</span></dt><dd><p>The condition number of the matrix. May be infinite.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="numpy.linalg.norm.html#numpy.linalg.norm" title="numpy.linalg.norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">numpy.linalg.norm</span></code></a></p>
</div>
<p class="rubric">Notes</p>
<p>The condition number of <em class="xref py py-obj">x</em> is defined as the norm of <em class="xref py py-obj">x</em> times the
norm of the inverse of <em class="xref py py-obj">x</em> <a class="reference internal" href="#r611900c44d60-1" id="id1">[1]</a>; the norm can be the usual L2-norm
(root-of-sum-of-squares) or one of a number of other matrix norms.</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r611900c44d60-1"><span class="brackets"><a class="fn-backref" href="#id1">1</a></span></dt>
<dd><p>G. Strang, <em>Linear Algebra and Its Applications</em>, Orlando, FL,
Academic Press, Inc., 1980, pg. 285.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">LA</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span>
<span class="go">array([[ 1,  0, -1],</span>
<span class="go">       [ 0,  1,  0],</span>
<span class="go">       [ 1,  0,  1]])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">1.4142135623730951</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="s1">&#39;fro&#39;</span><span class="p">)</span>
<span class="go">3.1622776601683795</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">)</span>
<span class="go">2.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">)</span>
<span class="go">1.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="go">2.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">1.0</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">1.4142135623730951</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">LA</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">)</span>
<span class="go">0.70710678118654746 # may vary</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">min</span><span class="p">(</span><span class="n">LA</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">compute_uv</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span><span class="o">*</span><span class="nb">min</span><span class="p">(</span><span class="n">LA</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">LA</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">a</span><span class="p">),</span> <span class="n">compute_uv</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
<span class="go">0.70710678118654746 # may vary</span>
</pre></div>
</div>
</dd></dl>

</div>


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